Boaz Porat

Estimation and classification of polynomial-phase signals

The measurement of the parameters of complex signals with constant amplitude and polynomial phase, measured in additive noise, is considered. A novel new integral transform that is adapted for signals of this type is introduced. This transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance. The algorithms are extended to constant amplitude and continuous nonpolynomial phase signals. >

Adaptive comb filtering for harmonic signal enhancement

A new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise. The algorithm is composed of two cascaded parts. The first estimates the fundamental frequency and enhances the harmonic component in the input. The second estimates the harmonic amplitudes and phases. Performance analysis provides new results for the asymptotic Cramer-Rao bound (CRB) on the parameters of harmonic signals with additive white noise.

Direction finding algorithms based on high-order statistics

Two direction finding algorithms are presented for nonGaussian signals, which are based on the fourth-order cumulants of the data received by the array. The first algorithm is similar to MUSIC, while the second is asymptotically minimum variance in a certain sense. The first algorithm requires singular value decomposition of the cumulant matrix, while the second is based on nonlinear minimization of a certain cost function. The performance of the minimum variance algorithm can be assessed by analytical means, at least for the case of discrete probability distributions of the source signals and spatially uncorrelated Gaussian noise. The numerical experiments performed seem to confirm the insensitivity of these algorithms to the (Gaussian) noise parameters. >

Analysis of the asymptotic relative efficiency of the MUSIC algorithm

An analytical performance evaluation of the errors of the direction-of-arrival estimates obtained by the MUSIC algorithm for uncorrelated sources is provided. Explicit asymptotic formulas are derived for the means and the covariance of the estimates. The covariances are then compared to the Cramer-Rao lower bound. It is shown that for a single course, the MUSIC algorithm is asymptotically efficient. For multiple sources, the algorithm is not efficient in general. However, it approaches asymptotic efficiency when the SNRs (signal-to-noise ratios) of all sources tend to infinity. It is illustrated by several test cases that the relative efficiency of the MUSIC algorithm is nearly one under a wide range of parameter variations. The analytic performance evaluation thus confirms empirical evidence to the excellent performance of the MUSIC algorithm for narrowband signals. >

Detection of transient signals by the Gabor representation

Gabor representation is used for the detection of transient signals with unknown arrival times. A one-sided exponential window function is used which seems to be most appropriate for transient modelling. Explicit expressions for the Gabor coefficients are given for this window function. When the given signal is random, so are the coefficients. The second-order moments of the Gabor coefficients are computed for a white noise signal. These are then used to introduce a detection statistic based on the Gabor coefficients. The proposed detector is capable of separating transients having different arrival times, even in this case where their waveforms partially overlap. >

A unified texture model based on a 2-D Wold-like decomposition

A unified texture model that is applicable to a wide variety of texture types found in natural images is presented. This model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters. The texture field is assumed to be a realization of a regular homogeneous random field, which is characterized in general by a mixed spectral distribution. The texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component. The deterministic component is further orthogonally decomposed into a harmonic component, and a generalized-evanescent component. Both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component. The model is very efficient in terms of the number of parameters required to faithfully represent textures. Reconstructed textures are practically indistinguishable from the originals. >

The Modified Yule-Walker Method of ARMA Spectral Estimation

An overview of ARMA spectral estimation techniques based on the modified Yule-Walker equations is presented. The importance of using order overestimation, as well as of using an overdetermined set of equations, is emphasized. The Akaike information criterion is proposed for determining the equation order. A procedure for removing spurious noise modes based on modal decomposition of the sample covariance matrix is derived. The role of the singular value decomposition method in solving the modified Yule-Walker equations is discussed. A number of techniques for estimating MA spectral parameters are presented.

Blind equalization of digital communication channels using high-order moments

The authors describe algorithms for blind equalization of digital communication channels of the quadrature-amplitude-modulation (QAM) type. These algorithms are based on the fourth-order statistical moments of the received data sequence. The first of the two is a linear least-squares-type algorithm. The second algorithm is of the nonlinear least-squares-type. The algorithms use the fourth-order statistical moments of the symbol sequence to explicitly estimate the channel impulse response. The estimated impulse response is used, in turn, to construct a linear mean-square error equalizer. The performance of this equalizer is not optimal in any sense, but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large. >

Asymptotically optimal estimation of MA and ARMA parameters of non-Gaussian processes from high-order moments

A description is given of an asymptotically-minimum-variance algorithm for estimating the MA (moving-average) and ARMA (autoregressive moving-average) parameters of non-Gaussian processes from sample high-order moments. The algorithm uses the statistical properties (covariances and cross covariances) of the sample moments explicitly. A simpler alternative algorithm that requires only linear operations is also presented. The latter algorithm is asymptotically-minimum-variance in the class of weighted least-squares algorithms. >

Square root covariance ladder algorithms

Square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting. A simplified derivation of the general update formulas for such ladder forms is presented, and is used to develop the growing memory and sliding memory covariance ladder algorithms. New ladder form realizations for the identified models are presented, leading to convenient methods for computing the model parameters from estimated reflection coefficients. A complete solution to the problem of possible singularity in the ladder update equations is also presented.